DRAFT September 21, 2021 Preprint typeset using LATEX style emulateapj v. 5/2/11

THE X-RAY LUMINOSITY FUNCTION OF M37 AND THE EVOLUTION OF CORONAL ACTIVITY IN LOW-MASS Alejandro Núñez1 and Marcel A. Agüeros1 DRAFT September 21, 2021

ABSTRACT We use a 440.5 ks Chandra observation of the ≈500-Myr-old M37 to derive the X-ray luminosity functions of its ≤1.2 M stars. Combining detections of 162 M37 members with upper limits for 160 non-detections, we find that its G, K, and M stars have a similar median (0.5−7 keV) X- 29.0 −1 ray luminosity LX = 10 erg s , whereas the LX-to-bolometric-luminosity ratio (LX/Lbol) indicates that M stars are more active than G and K stars by ≈1 order of magnitude at 500 Myr. To characterize the evolution of magnetic activity in low-mass stars over their first ≈600 Myr, we consolidate X-ray and optical data from the literature for stars in six other open clusters: from youngest to oldest, the Orion Cluster (ONC), NGC 2547, NGC 2516, the Pleiades, NGC 6475, and the . For these, we homogenize the conversion of instrumental count rates to LX by applying the same one- temperature emission model as for M37, and obtain masses using the same empirical mass-absolute magnitude relation (except for the ONC). We find that for G and K stars X-ray activity decreases ≈2 orders of magnitude over their first 600 Myr, and for M stars, ≈1.5. The decay rate of the median LX b follows the relation LX ∝ t , where b = −0.61±0.12 for G, −0.82±0.16 for K, and −0.40±0.17 for M stars. In LX/Lbol space, the slopes are −0.68±0.12, −0.81±0.19, and −0.61±0.12, respectively. These results suggest that for low-mass stars the age-activity relation steepens after ≈625 Myr, consistent with the faster decay in activity observed in solar analogs at t > 1 Gyr. Subject headings: : open clusters and associations: individual (M37) – stars: activity – stars: coronae – stars: low-mass – X-rays: individual (M37)

1. INTRODUCTION strength, appears to evolve differently (e.g., Jackson & < Jeffries 2010; Douglas et al. 2014) but may suffer a simi- In low-mass stars (∼1 M ), X rays originate in a mag- netically heated corona, and serve as a proxy for the larly steep decline for t > 1 Gyr (Pace & Pasquini 2004). > strength of the magnetic dynamo2. The X-ray lumi- To determine the evolution of LX, we need more ∼200- Myr-old open clusters with well-characterized cumula- nosity, LX, is correlated with age and rotation (e.g., Pallavicini et al. 1981; Pizzolato et al. 2003), and de- tive X-ray luminosity functions (XLFs). In Núñez et al. creases as low-mass stars spin down because of the loss (2015, hereafter Paper I), we described our 440.5 ks of angular momentum through magnetized winds. Cali- Chandra observation of M37 (NGC 2099), a rich, ≈500- Myr-old cluster at a distance of 1490±120 pc (Hartman brating the evolution of LX is key to quantifying the in- terplay between stellar rotation and magnetic fields, and et al. 2008b). We combined the photometry compiled ultimately to uncovering the still-mysterious processes by Hartman et al. (2008a, hereafter HA08) and distance responsible for these fields. from the cluster core to generate membership proba- bilities (Pmem) for cluster stars. Our final catalog in- Observations indicate that LX does not decay smoothly with age (t). Surveys of solar-type stars in the cluded 561 X-ray sources with optical counterparts, 278 Pleiades (t ≈ 125 Myr) and the Orion Nebula Cluster of which had Pmem ≥ 0.2. Here, we add to these detec- (ONC; 1−10 Myr) concluded that L falls off relatively tions LX upper limit (UL) measurements for undetected X members to determine the XLFs for M37’s G, K, and M slowly early in a ’s life: L ∝ t−0.76 (Queloz et al. X stars. We also compute bolometric luminosities (L ), 1998; Preibisch & Feigelson 2005). Because there are few bol and use these to determine the L /L functions (LLFs) accessible t > 200 Myr clusters, constraints are harder to X bol arXiv:1607.05789v2 [astro-ph.SR] 29 Oct 2016 ∼ for these stars, thereby establishing M37 as the bench- come by for older stars, but from observations of five solar mark 500-Myr-old cluster for studies of the evolution of analogs, Güdel et al. (1997) determined that L ∝ t−1.5 X X-ray emission in low-mass stars. for t > 1 Gyr, as did Giardino et al. (2008) from their sur- In Section 2, we describe our optical and X-ray data vey of the ≈1.5-Gyr-old cluster NGC 752. Core-envelope for M37, outline how we assign membership thresholds decoupling or a change in the magnetic field topology for inclusion in our analysis, and calculate L ULs for are the commonly invoked explanations for this sharp X undetected sources. In Section 3, we construct the XLFs drop off in L (e.g., Kawaler 1988; Krishnamurthi et al. X and LLFs and discuss the impact of our upper limits and 1997), but it remains poorly understood. Interestingly, of binaries on these functions. In Section 4, we first ho- chromospheric activity, another proxy for magnetic field mogenize the LX, Lbol, and masses of stars in six other clusters ranging in age from 6 to 625 Myr. We then ex- 1 Department of Astronomy, Columbia University, 550 West amine the evolution of the XLFs and LLFs for GKM stars 120th Street, New York, NY 10027, USA over ≈600 Myr. We present our conclusions in Section 2 For a recent review of the connection between stellar activity and coronal heating, see Testa et al. (2015). 5. 2 Núñez & Agüeros

2. CHARACTERIZING LOW-MASS STARS IN M37 TABLE 1 2.1. Setting the Thresholds for Cluster Membership M37 Low-Mass Members in the Field of View of Chandra HA08 obtained gri images of a 240×240 area centered on a b d f ID Pmem Bin. Mass log(Lbol) Det. log(LX) M37 with Megacam on the 6.5-m MMT telescope at the c −1 e −1 MMT Observatory, AZ. In Paper I, we used this photom- flag (M )(erg s ) flag (erg s ) etry and the distance from the cluster core for ≈16,800 30118 0.48 0 0.61 32.55 0 29.63 HA08 objects to identify cluster members. Each star was 40031 0.42 0 0.98 33.26 0 29.52 40039 0.41 0 0.88 33.12 0 29.62 assigned a probability of being a single member (Ps), a 40097 0.41 0 0.66 32.72 0 29.67 likely binary member (Pb), or a field star (Pf ), with Ps 40103 0.60 0 0.63 32.66 0 29.57 + P ≡ P and P + P + P = 1 for each star. We b mem s b f Note. — This table is available in its entirety in the electronic identified 1643 stars with Pmem ≥ 0.2, which we used as edition of the ApJ. The first five rows are shown here for guidance the Pmem cutoff for cluster membership (see section 3.3 regarding its form and content. a Source ID from HA08. and appendix A of Paper I). b Using such a low P threshold increases the like- Membership probability, recalculated for this study. mem c Binary flag from Paper I: 0, likely single star; 1, likely binary. lihood of field-star contamination: for example, only d Bolometric luminosity from Paper I. e 20−30% of the stars in the 0.2 ≤Pmem< 0.3 bin should Detection flag: 0, undetected in X ray; 1, detected in X ray. f be bona fide cluster members. However, because M37 LX (LX UL) in the 0.5−7 keV band for detected (undetected) stars are much more likely to be bright X-ray emitters objects calculated as described in Section 2.3 (2.4). than their older field-star cousins, we consider all X-ray ble 1 lists all low-mass M37 stars with Pmem ≥ 0.2, al- emitters with Pmem > 0.2 to be cluster members and now though only those with Pmem ≥ 0.7 were used in our assign these stars Pmem = 1.0. study. Column 1 is the source ID of the optical object In effect, this redistributes absolute Pmem points from from HA08; Column 2 is the recalculated Pmem; Column the non-detections to the X-ray emitters by the total 3 is a binary flag set to 1 if the object is likely a binary P quantity q = i(1− Pmem,i), where i is the number of (see appendix A in Paper I) and 0 otherwise; Column 4 is X-ray emitters in each Pmem bin (0.2 ≤ Pmem< 0.3, 0.3 ≤ mass; Column 5 is Lbol; Column 6 is a detection flag set Pmem< 0.4, and so on). We therefore also decrease the to 1 if the object has an X-ray detection and 0 otherwise Pmem values of non-detections by subtracting the quan- (i.e., a non-detection); Column 7 is the LX of detections tity q/N from their original Pmem, where N is the number or the LX ULs of non-detections (see discussion below). of non-detections in each Pmem bin. While we could simply use the original Pmem ≥ 0.2 2.3. Calculating LX for Detected Members threshold for non-detections, there is no way to distin- We described our source detection procedure in Paper guish bona fide members that are X-ray-undetected from I. Briefly: we used wavdetect in the Chandra Interactive field contaminants in low Pmem bins. We therefore ap- Analysis of Observations (CIAO Fruscione et al. 2006) ply a more conservative Pmem ≥ 0.7 cutoff to minimize tool and the ACIS Extract point-source analysis software the risk of biased results. Finally, we note that for (AE version 2014feb17; Broos et al. 2010). We found stars outside the field-of-view of our Chandra observa- 774 X-ray sources, 278 of which were matched to cluster tion Pmem ≤ 0.4, so that the completeness of our sample members. For each source we calculated net counts in is not affected by excluding these stars. the 0.5−7 (full), 0.5−2.0 (soft), and 2.0−7.0 (hard) keV energy bands. 2.2. Assigning Masses and Estimating L bol In Paper I, we converted net count rates into absorbed To estimate masses for M37 stars, we first used the r energy fluxes by calculating the incident flux3 in the soft photometry of HA08, along with the cluster reddening and hard bands, and then multiplying the median photon E(B − V ) = 0.227 and distance of 1490 pc obtained by energy in each band by its incident flux. The absorbed these authors, to calculate an absolute r magnitude Mr energy flux in the full band is the sum of the energy fluxes for each member. We then applied the Mr-mass relation of the soft and hard bands. Using the mass bins defined of Kraus & Hillenbrand (2007), who generated empiri- in Section 2.2, we detected 59 G, 36 K, and 67 M cluster cal spectral energy distributions for B8-L0 stars that are stars. The faintest X-ray emitting M37 member has a calibrated using the 600-Myr-old Praesepe cluster and mass of 0.26 M . Sloan Digital Sky Survey (SDSS, York et al. 2000) ugriz To compare our results to those for other clusters, we and Two Micron All Sky Survey (2MASS, Skrutskie et al. recalculate energy fluxes of cluster members by convert- 2006) JHK photometry (see section 4.1.1 of Paper I). ing net count rates into unabsorbed 0.5−7 keV fluxes We estimate Lbol for M37 members by first using the using WebPIMMS.4 We assume an atomic neutral hydro- 21 −2 Mr-effective temperature (Teff ) relation of Kraus & Hil- gen column density NH = 1.26×10 cm , derived from −2 lenbrand (2007). After obtaining Teff for each star, we E(B −V ) = 0.227 (HA08), RV = 3.1, and NH[cm /Av] use the corresponding bolometric correction in the Gi- = 1.79 ×1021 (Predehl & Schmitt 1995). We apply a rardi et al. (2004) tables, which we tailor to the SDSS thermal (APEC) model, setting the abundance to 0.4 of filter system. This allows us to calculate bolometric mag- solar. This choice of a sub-solar abundance is justified nitudes and luminosities, the latter by again using the by observations of very active stars, whose coronal abun- distance to the cluster of 1490 pc. dances range from 0.3−0.5 of solar (e.g., Briggs & Pye There are 118 M37 stars with Pmem ≥ 0.7 and masses 0.8−1.2 M , 125 with masses 0.6−0.8 M , and 79 with 3 The incident flux is the net counts divided by the mean Aux- masses 0.1−0.6 M , corresponding approximately to G, iliary Response File divided by the exposure time. K, and M stars, respectively (Cram & Kuhi 1989). Ta- 4 http://cxc.harvard.edu/toolkit/pimms.jsp M37 and the Evolution of X-ray Emission in Low-Mass Stars 3

2003; Güdel 2004; Telleschi et al. 2005; Jeffries & Oliveira )

1 brightest 2005). − V sources e 4

We decided to use a one-temperature (1T) model after k

1 1T model fitting spectra of the 10 brightest and of the 40 faintest − s

5 cluster sources with 1T and two-temperature (2T) mod- t 2T model c 5 (

log(T/K) = 7.09 0.01 els, and keeping the value of NH fixed. Figure 1 shows e ± t χ 2 = 1.34 / d.o.f. = 80 a ν the results: the 2T fits are not a statistical improvement r t 6 n

on the 1T fits. In addition, the 2T model does not per- u log(T1 /K) = 7.12 0.02 o ± c

form well with the brightest sources, as the lower of the log(T2 /K) 4.97 g 2 ≈ o 7 two temperatures is unreasonably cool (log(T /K) = 4.97) l χν = 1.36 / d.o.f. = 78 and likely a result of the fit hitting a hard floor limit. 2 Furthermore, the 2T fit for the faintest sources produces 0 res a relatively large uncertainty for the high-temperature 2 0 component (log(T2/K) = 7.20±0.21). ) 10 1 faintest A 1T model is therefore an adequate approximation − 5 V sources e

of the plasma temperature for X-ray-emitting members k

1 of M37. This is consistent with findings in the litera- − s

6 ture: typically, 2T fits return plasma temperatures of t c (

log(T/K) = 6.88 0.03 log(T1/K) ≈ 6.7 and log(T2/K) ≈ 7.2 but differ statis- e ± t χ 2 = 1.23 / d.o.f. = 28 a ν tically very little from simpler 1T models with a tem- r

t 7 n

perature between these two values. This is particularly u log(T1 /K) = 7.20 0.21 o ± c true for low-count sources (Schmitt et al. 1990; Jeffries log(T2 /K) = 6.87 0.08 g 2 ±

o 8 & Oliveira 2005), and 99% of our X-ray counterparts l χν = 1.28 / d.o.f. = 26 to low-mass M37 stars have <100 counts. Furthermore, 2 100 other studies have found that adopting one plasma tem- 0 res perature in the log(T /K) ≈ 6.9−7.1 range is adequate for 2 characterizing the underlying differential emission mea- 0.5 1 2 5 sure in coronae of fairly active stars detected as low-count energy (keV) X-ray sources (Gagne et al. 1995; James & Jeffries 1997; Fig. 1.— Spectral fits for stacks of the 10 brightest (upper panel) Jeffries et al. 2006; Pillitteri et al. 2006). and 40 faintest (lower panel) M37 sources using 1T (blue solid We set log(T /K) = 7 (kT = 0.8617 keV), which is the line) and 2T (red dashed line) APEC models, assuming 0.4 solar 6 21 −2 average of our two 1T models’ best-fit temperatures. abundance and NH = 1.26×10 cm . The fits are drawn over the The median L of our M37 sample changes by 0.12 dex if binned data (10 counts per bin; black circles). Error bars are too X small to show. For each fit, we give the resulting temperature(s) of we go from adopting log(T /K) = 6.9 to log(T /K) = 7.1. 2 the APEC model, the reduced chi-squared statistic (χν ), and the We are adding <1% in uncertainty to our LX calcula- degrees of freedom (d.o.f.). Residuals are shown below each panel, tions by adopting this single coronal temperature for all normalized by the stacked spectrum counts. There is no evidence sources. from these fits that a 2T model is required to represent these data. and the area of the annulus, we calculate the background 2.4. Calculating L for the Non-Detections X in counts per second per pixel squared, from which we We calculate LX ULs for the 160 undetected low-mass then estimate the background inside the inner radius of stars with Pmem ≥ 0.7 within the field of view of our the annulus, the actual region of the undetected source. Chandra observation. We follow Kashyap et al. (2010) We convert the resulting UL count rates into unab- and define an UL as the maximum LX a source can sorbed X-ray fluxes with WebPIMMS by applying the have without exceeding some detection threshold with same model and parameters described in Section 2.3 for a given probability, given a specified background. We members with X-ray detections. In Table 1 we list the 6 use a detection threshold of 10 (equivalent in CIAO LX UL of all undetected stars with Pmem ≥ 0.2, although −6 to wavdetect’s threshold significance of 10 , the value only stars with Pmem ≥ 0.7 were included in our analysis. used in the source detection procedure in Paper I) and a false negative probability of 0.5. 2.5. The Impact of ULs on the XLFs To estimate the background of each undetected source, To define the XLFs and LLFs, we use the Kaplan- we draw an annulus with ds9 centered on its optical Meier (K-M) method as implemented in the lifelines counterpart’s coordinates. We set the inner radius of the package (Davidson-Pilon 2016), and treat ULs as left- annulus to the size of the point source function (PSF) censored data points. We apply Efron’s bias correction that encloses 100% of counts from a point source at that (Efron 1967), which considers the lowest LX value to be location, and the outer radius to three times that size. a detection even if it is not. Our M37 sample contains We use CIAO’s dmlist to find the number of 0.5−7 keV a significant number of X-ray ULs: in the most extreme counts in the annulus, and dmstat to find the mean expo- case, 71% of the K stars with Pmem ≥ 0.7 are unde- sure time for that region. Combining these two quantities tected. This is concerning because the K-M method is biased when censored data represent a very large fraction 5 Stacking is necessary because almost all of our detections have <<100 counts. of the whole sample (e.g., Huynh et al. 2014). 6 In the Appendix, we discuss further tests we conducted to To test the impact of ULs, we re-calculate the XLFs af- examine the impact of assuming a constant plasma temperature ter varying the Pmem cutoff, which, since all X-ray detec- for our stars regardless of their age. tions have Pmem = 1, is equivalent to varying the number 4 Núñez & Agüeros of censored data points in the sample. As an example, we emission are obvious here, with the fraction produced in show in Figure 2 the impact on the K-star XLF when we X rays becoming significantly smaller as mass increases. vary the Pmem cutoff from 0.2 to 0.9 in 0.1 increments. Finally, to the right of the panels, boxplots for each We also show the XLF we obtain including only detec- mass bin extend from the lower to the upper quartile; tions. Finally, we indicate the median LX from each K-M the whiskers cover the entire data range, and medians solution with a vertical arrow. are indicated by a horizontal line inside the boxes. More massive stars clearly have lower intrinsic activity levels 1.0 than their least massive cousins. K stars 3.1. The Impact of Binaries 0.6 0.8 M − ¯ In Paper I we flagged a star as a likely M37 binary if 0.8 Pb > Ps and Pb +Ps ≥ 0.2, where Pb was based on height Pmem cutoff: from the in the (i,g − i) color-magnitude 0.2 diagram. Since stars in our M37 sample flagged as likely 0.3 binary remain unresolved, we are, therefore, potentially 0.6 0.4 overestimating their stellar masses, as we derived masses 0.5 using the combined photometry of the system. 0.6 Furthermore, some low-mass stars may remain hid- 0.7 den in binaries with a massive companion. This is cor- 0.4 roborated by our detection in X rays of 104 high-mass 0.8 cluster members. X-ray emission from such systems is 0.9 more likely to come from a low-mass companion (see e.g., detections only Preibisch & Zinnecker 2002), and indeed 39 of the 104 0.2 are photometric candidate binaries, suggesting that our sample of M37 low-mass stars is incomplete. The 44 detected low-mass candidate binaries are also Cumulative distribution function (Kaplan-Meier) difficult to interpret. The X-ray emission from such sys- 0.0 tems could potentially come from both components, and 28.5 29.0 29.5 30.0 so counting each detection as just one source could bias log(L ) (erg s 1 ) X − the XLFs and LLFs toward higher luminosities. Fig. 2.— K star XLFs for Pmem cutoff values ranging from 0.2 We calculate the XLFs by excluding all likely binaries to 0.9 in 0.1 increments. Our adopted cutoff, Pmem ≥ 0.7, is the in our sample and compare the results with those in Fig- bold solid black XLF. The K-M solution for the sample including ure 3. We find very small differences in the K-M solutions detections only is in dashed gray. The median log(LX) for each K-M solution is indicated with a vertical arrow. of the samples including and excluding likely binaries. In the extreme case, the median log(LX) of cluster M stars Having a large number of censored data points biases shifts by 0.05 dex when likely binaries are excluded. Fur- thermore, since potential contamination by binaries is an the XLF toward lower LX values. It appears, however, < issue for all XLF studies, and since the binary fraction for that implementing a Pmem cutoff ∼0.8 has little effect on the shape of the XLF. In the extreme case, the dif- open clusters and over time does not vary significantly (Duchêne & Kraus 2013), we simply include binaries in ference in median LX between a sample of K stars with P > 0.2 and one of P > 0.9 K stars is ≈0.2 dex. the construction of the XLFs and LLFs of M37 and of all mem mem other clusters in our study. For G and M stars, the difference in median LX between these two Pmem cutoffs is ≈0.1 dex. We conclude that 4. THE EVOLUTION OF X-RAY ACTIVITY the impact of ULs as a function of Pmem cutoff, and thus X-ray activity decreases with time in low-mass main- of the fraction of ULs in a given mass bin, on the K-M sequence stars (e.g., Güdel et al. 1997; Preibisch & Feigel- statistics is limited to a shift of at most 0.2 dex. son 2005; Giardino et al. 2008). To quantify this evolu- tion, we compare the XLFs and LLFs we obtain for M37 3. X-RAY ACTIVITY AT 500 MYR to those for six other open clusters: the ONC (0.1−10 The left panel of Figure 3 shows the XLFs of stars Myr, Preibisch & Feigelson 2005), NGC 2547 (35±3 Myr, with Pmem ≥ 0.7 for the G (solid blue), K (dotted or- Jeffries & Oliveira 2005), NGC 2516 (120 ± 25 Myr, Silaj ange), and M stars (dashed red). The median values & Landstreet 2014), the Pleiades (125 ± 8 Myr, Stauffer are indicated with vertical arrows. G and M stars have et al. 1998), NGC 6475 (220±50 Myr, Silaj & Landstreet the highest median LX values from the K-M solution, 2014), and the Hyades (625±50 Myr, Perryman et al. −1 log(LX/erg s ) ≈ 29.0, while for K stars it is ≈28.9. 1998). All six clusters have well-defined membership cat- All three classes have very similar lower−upper quartile alogs that extend to the low-mass end and have been sur- −1 levels: log(LX/erg s ) = 28.8−29.2 for G and K stars veyed extensively in the X ray, rendering a meaningful and 28.9−29.2 for M stars. This suggests that at an age comparison to each other and to M37 possible. of 500 Myr, LX is fairly constant for low-mass stars. The published LX values from the surveys of these clus- The center panel of Figure 3 compares the LLFs for ters differ in terms of the quoted energy bands and how the three mass bins. Calculating LX/Lbol allows us to they were obtained from the instrumental count rates. remove the mass dependence of LX and reveal the frac- To homogenize the X-ray data, we use the original count tion of the stars’ total emission that is in the X ray. The rates of all sources and, as with our M37 sources, ap- differences in the X-ray contribution to the overall stellar ply a 1T APEC model with 0.4 solar abundance and M37 and the Evolution of X-ray Emission in Low-Mass Stars 5

1.0 30.5 2.5 G stars K stars G M stars 3.0 0.8 30.0

K 3.5 ) 1 − )

0.6 l s o M b g L r

29.5 / e X ( 4.0

L )

M ( X g

L K o ( 0.4 l g o l 4.5 29.0

0.2 5.0 G

Cumulative distribution function (Kaplan-Meier) 28.5 0.0 5.5 28.5 29.0 29.5 30.0 5.0 4.5 4.0 3.5 3.0 L ) L /L ) 1 log( X log( X bol log(LX) (erg s− ) log(LX/Lbol)

Fig. 3.— K-M estimator for the XLFs (left panel) and LLFs (center panel) of M37 G (solid blue line), K (dotted orange), and M (dashed red) stars. The median value for each K-M solution is indicated with a vertical arrow. To the right of the panels, boxplots for each mass bin extend from the lower to the upper quartile; the whiskers cover the entire data range. The horizontals lines are the median values.

TABLE 2 Cluster Characteristics And Number of X-ray Detections/Non-Detections

a b d d d Name Ref Inst. log(LX) G Stars K Stars M Stars log(age) Distance log(NH) E(B − V ) Minc D ND D ND D ND (Myr) (pc) (cm−2)

ONC 1 CA 27.48 10 0 7 0 138 0 6.41f 414.0 21.72f ...g NGC 2547 2,3 RH,X 28.83 27 0 19 0 44 0 7.54 407.0 20.48 0.038 NGC 2516e 4 X 28.53 70 56 29 49 96 174 8.08 385.5 20.90 0.120 Pleiadese 5,6,7 RP,RH 28.00 74 23 58 22 88 137 8.10 136.2 20.40 0.032 NGC 6475 8,9,10 RP,X 28.64 37 0 51 1 6 0 8.34 302.0 20.54 0.060 M37 11 CA 28.45 59 59 36 89 67 12 8.69 1490.0 21.10 0.227 Hyades 12,7 RP 27.50 65 12 27 28 54 39 8.80 47.3f <20.00 0.000 a Reference for X-ray data: (1) Getman et al. (2005); (2) Jeffries & Tolley (1998); (3) Jeffries & Oliveira (2005); (4) Pillitteri et al. (2006);(5) Stauffer et al. (1994); (6) Micela et al. (1999); (7) Stelzer et al. (2000); (8) Prosser et al. (1995); (9) James & Jeffries (1997); (10) Obs. ID 0300690101 in 3XMM-DR5 Catalog; (11) Paper I; (12) Stern et al. (1995). b X-ray instrument: CA = Chandra ACIS; X = XMM EPIC; RP = ROSAT PSPC; RH = ROSAT HRI. c −1 Minimum log(LX) value detected in erg s (0.5−7.0 keV band). d Number of detections (D) and non-detections (ND). G stars: 0.8−1.2 M ; K stars: 0.6−0.8 M ; M stars: 0.1−0.6 M . e We combine these two to create the representative ≈120-Myr-old cluster used in our analysis. f Mean value for cluster stars. g No reddening value adopted. log(T /K) = 7 (see further discussion of the assumed T tance and reddening for each cluster. We use these to value in the Appendix) to obtain unabsorbed 0.5−7 keV calculate LX and NH, following the reddening-NH rela- fluxes. tion of Bohlin et al. (1978). As discussed in Section 2.3, our choice of plasma tem- To determine the stars’ masses, we first combine perature is appropriate for low-count X-ray sources of BVRIJHK or ugriz photometry, cluster distances, and fairly active stars, which describes most stars in these total absorption in each band7 to obtain absolute mag- surveys. Furthermore, even though coronal temperatures nitudes. We then apply the absolute magnitude-mass are found to decrease with stellar age (e.g., Telleschi et al. relations of Kraus & Hillenbrand (2007); for stars with 2005, who found that for solar analogs these tempera- only BVRI photometry, we use the extended version of tures decrease by 0.37 dex between 0.1 and 0.75 Gyr), the same relations described in Agüeros et al. (in prep). the uncertainty introduced by adopting the same tem- For the ONC we adopt the stellar masses of Getman et al. perature for the entire 6−625 Myr range is not signifi- (2005), which were derived using the pre-main-sequence cant, given the low counts of our sources. Overall, 54% (PMS) evolutionary tracks of Siess et al. (2000). of the X-ray sources in the surveys considered here have fewer than 100 counts, and 81% fewer than 500. 7 We use the extinction tables of Schlafly & Finkbeiner (2011) We also found the most up-to-date estimation of dis- assuming RV = 3.1 and adopting E(B − V ) values. 6 Núñez & Agüeros

Finally, we use a linear interpolation between the stel- 0.3−3.0 keV band for 49.4 ks; Jeffries et al. (2006) re- lar mass-Lbol values for M37 (see Section 2.2) to estimate ported 108 detections. In addition, Jeffries et al. (2006) Lbol for stars in the other clusters. modified the original ROSAT count rates to apply a more Table 2 summarizes the basic characteristics of these sophisticated PSF model for the HRI instrument. six clusters and those of M37, and gives for each the num- Seventy-two cluster stars are detected in both observa- ber of detections and non-detections in each mass bin. tions, 36 only by XMM, and two only by ROSAT, for a Table 3 lists all low-mass cluster members with their de- total of 110 low-mass NGC 2547 stars with X-ray detec- rived stellar masses, Lbol, distances, NH values derived tions. For the XMM sources, we use time-weighted mean from E(B − V ), and LX values for detected sources and count rates from their pn, MOS1, and MOS2 count rates. LX ULs for undetected sources. Below we briefly sum- For the ROSAT sources, we use the modified count rates marize the X-ray observations for each cluster and the of Jeffries et al. (2006). For stars detected in both obser- cluster parameters we assumed to perform our analysis. vations, we obtain a combined LX using a weighted av- erage of the two separate LX values. We adopt d = 407 −2 4.1. The Comparison Set of Clusters pc (Mayne & Naylor 2008), log(NH/cm ) = 20.48 (Jef- 4.1.1. The ONC fries & Oliveira 2005), and E(B − V ) = 0.038 (Mayne & Naylor 2008) for all cluster stars. At 0.1−10 Myr in age (we adopt 6 Myr), the ONC The vast majority of NGC 2547’s low-mass stars are de- serves as an essential young benchmark for studies of the tected. All those with 1.4 < (V −I) < 2.5 (≈K5−M3) are long-term evolution of X-ray activity (e.g., Preibisch & detected, and only a handful of stars near (V − I) ≈ 1.2 Feigelson 2005; Jeffries et al. 2006) because of its well- and an increasing number of stars at (V − I) > 2.8 described membership and extensive X-ray coverage. We remained undetected. Jeffries et al. (2006) therefore therefore include the ONC in our comparison, albeit with did not account for non-detections. The faintest cluster two caveats. First, practically all low-mass stars in the member detected in X rays has a mass of 0.32 M . ONC are in the PMS phase and therefore still contracting and spinning up. Second, at such young ages low-mass 4.1.3. NGC 2516 stars are still likely to be surrounded by inner circumstel- Pillitteri et al. (2006) used two different XMM point- lar disks, which may either obscure or enhance stellar ings totaling 105.7 ks to observe the 120-Myr-old open X-ray emission (Bouvier et al. 1997; Wolff et al. 2004; cluster NGC 2516. These authors detected 258 mem- Preibisch et al. 2005). Considered all together, ONC bers (201 low-mass) and calculated 0.3−7.9 keV LX ULs stars therefore might not exhibit a clear X-ray rotation- for 354 (287 low-mass) that remained undetected.8 The activity relation (Krishnamurthi et al. 1997; Feigelson faintest cluster member detected in X rays has a mass of et al. 2003). To select a sample of ONC stars comparable 0.19 M ; the same is true for the faintest cluster member to those in older clusters, we exclude from our analysis with an LX UL measurement. In cases where Pillitteri stars that show evidence of having either a circumstel- et al. (2006) matched an X-ray source to more than one lar disk or strong accretion (see sections 8.1 and 8.2 of cluster star, we assume the X-ray emission to originate Preibisch et al. 2005). from the closest match only. Getman et al. (2005) presented a 838 ks Chandra obser- We adopt d = 385.5 pc (Terndrup et al. 2002), vation of the ONC. These authors detected >1600 point −2 log(NH/cm ) = 20.90 (Pillitteri et al. 2006), and E(B− sources in the 0.5−8 keV band. Following Preibisch et al. V ) = 0.12 (Dachs & Kabus 1989) for all cluster stars. (2005), we adopt the masses derived by Getman et al. (2005) using the theoretical PMS evolutionary tracks of 4.1.4. The Pleiades Siess et al. (2000). There are 478 low-mass ONC stars, The Pleiades was surveyed with ROSAT on at least 155 of which show no evidence for circumstellar disks or three occasions. Stauffer et al. (1994) first observed the strong accretion. We use the published Chandra ACIS cluster with the PSPC instrument (0.15−2.0 keV) using net counts, exposure times, and NH values for each of three different pointings for a total of 73.5 ks. These these 155 sources to calculate their LX. We adopt a dis- authors detected 176 cluster members, and calculated tance d = 414 pc (Menten et al. 2007) for all stars in the LX ULs for 62 more members that remained undetected. cluster. Micela et al. (1999) reported several observations of the Preibisch et al. (2005) reported >98% of low-mass Pleiades with the ROSAT HRI instrument (0.1−2.4 keV) ONC stars as X-ray sources, and there is therefore no using eight different pointings for a total of 234.7 ks. need to account for non-detections. The optically faintest These authors detected 120 Pleiads, including 15 that cluster member detected in X rays has a mass of 0.10 M . were undetected by Stauffer et al. (1994). Micela et al. (1999) also calculated LX ULs for ≈90 members with no 4.1.2. NGC 2547 previous LX measurements. Although most low-mass stars in the 35-Myr-old clus- Finally, Stelzer et al. (2000) calculated 0.15−2.0 keV ter NGC 2547 are still in the PMS phase, there is evi- LX for 211 cluster members and LX ULs for 199 unde- dence that their inner circumstellar disks have dissipated tected ones using 10 publicly available ROSAT PSPC (e.g., Jeffries et al. 2000; Young et al. 2004). It is thus observations with a combined exposure time of 105.9 ks. expected that their X-ray emission be unobstructed and Sixty-eight of these LX measurements were of cluster more representative of main-sequence coronae. members with no previous X-ray detections. NGC 2547 was first observed with ROSAT HRI in the 8 NGC 2516 was observed with ROSAT by Jeffries et al. (1997) 0.1−2.4 keV band for 57.9 ks, resulting in 102 detec- and Micela et al. (2000) and with Chandra by Damiani et al. (2003); tions of cluster members Jeffries & Tolley (1998). The given the completeness and much higher sensitivity of the XMM cluster was observed again with XMM-Newton in the observation, we opt to use only the latter for simplicity. M37 and the Evolution of X-ray Emission in Low-Mass Stars 7

TABLE 3 Clusters Members Characteristics

a b c e Name α (J2000) δ (J2000) Cluster Mass log(Lbol) Distance NH Detection log(LX) ◦ −1 20 −2 d −1 ( )(M )(erg s ) (pc) (×10 cm ) flag (erg s ) COUP 6 83.65928 -5.40653 ONC 0.23 33.03 414 13.18 1 29.88 COUP 10 83.66681 -5.43448 ONC 0.13 33.23 414 1.00 1 28.68 COUP 14 83.67345 -5.39938 ONC 0.13 32.92 414 6.46 1 28.88 COUP 17 83.67930 -5.33534 ONC 0.90 33.86 414 13.18 1 30.18 COUP 20 83.68520 -5.43502 ONC 0.16 33.11 414 48.98 1 29.44 Note. — This table is available in its entirety in the electronic edition of the ApJ. The first five rows are shown here for guidance regarding its form and content. a Stellar mass derived from JHK or ugriz photometry using the mass-absolute magnitude relation of Kraus & Hillen- brand (2007) and extended for BRI photometry by Agüeros et al. (in prep). b Lbol derived from a linear interpolation between the stellar mass-Lbol relation in M37 stars, as described in Section 2.2. c Atomic neutral hydrogen column density; null if assumed to be negligible. d X-ray detection flag: (0) non-detection; (1) detection. e LX (LX UL) in the 0.5−7 keV energy band for detected (undetected) objects calculated using the method in Section 2.3. We match these sources to the updated membership 1.2 catalog of Covey et al. (2016). We obtain 265 Pleiads with detections and 211 with LX ULs, of which 220 and 1.0 182 are low-mass stars, respectively. For stars in more

than one X-ray study, we use the weighted average count ) 0.8 ¯

rate to calculate the LX. The faintest detected cluster M (

member and the faintest with an upper limit have a mass s s 0.6 of 0.12 M . We adopt d = 136.2 pc (Melis et al. 2014), a

M −2 log(NH/cm ) = 20.4 (Micela et al. 1999), and E(B−V ) 0.4 = 0.032 (An et al. 2007) for all cluster stars. An inspection of the Pleiades and NGC 2516 reveals 0.2 that the two clusters share several characteristics rele- vant to our study, including nearly identical XLFs for NGC 2516 non-detections all mass bins, similar low-mass populations with avail- 30.5 able X-ray data, and overlapping age estimates. Regard- NGC 2516 detections ing the latter, we note that both clusters have age es- Pleiades non-detections 30.0 Pleiades detections )

timates spanning the approximate range 65−150 Myr. 1 − s

For the Pleiades, several isochronal estimates indicate

g 29.5 r

an age near 125 Myr (e.g., Stauffer et al. 1998; David e (

& Hillenbrand 2015; David et al. 2016), but others re- ) X

L 29.0 turn ages as young as 75 Myr (Steele et al. 1993) or ( g o as old as 150 Myr (Mazzei & Pigatto 1989). Further- l more, lithium-depletion studies indicate ages of 112 Myr 28.5 (Dahm 2015) and 130 Myr (Barrado y Navascués et al. 2004). For NGC 2516, studies of magnetic Ap and Bp stars indicate an age of 120 Myr (Silaj & Landstreet 0 20 40 60 80 100 120 140 160 180 200 2014), which is similar to some isochronal age estimates Number (e.g., Kharchenko et al. 2005; Lyra et al. 2006), but lower Fig. 4.— Histograms with the number of low-mass detections and than others (e.g., 140 Myr, 158 Myr, Meynet et al. 1993; non-detections for the Pleiades (light and dark blue) and NGC 2516 Sung et al. 2002, respectively). (hashed orange and red) as a function of mass (top panel) and To simplify our analysis, we combine detections and log(LX) (bottom panel). For non-detections, the latter are ULs. non-detections from the Pleiades and NGC 2516 to create James & Jeffries (1997) reported a separate 27 ks a single, representative ≈120 Myr-old cluster, which we ROSAT PSPC (0.4−2.4 keV) observation of NGC 6475 consider to be a reasonable approximate age for stars in and the detection of 35 cluster stars, only four of which the two clusters. Figure 4 shows mass (top) and log(LX) are not among the Prosser et al. (1995) sources. Neither (bottom) histograms for the resulting cluster. of the ROSAT surveys reported LX ULs for low-mass stars. 4.1.5. NGC 6475 There is also an archival 46 ks XMM observation (Observation ID 0300690101, PI: R. Pallavicini) in This 220-Myr-old open cluster was observed by Prosser the 3XMM-DR5 catalog of serendipitous X-ray sources et al. (1995) with ROSAT PSPC (0.07−2.4 keV) using (Rosen et al. 2015), for which the Survey Science Cen- two different pointings for a total of 46.6 ks. These au- ter processing pipeline (version 4.1) returned 196 X-ray thors found at least one cluster optical counterpart to 129 point sources of good quality (i.e., quality flag = 0). We of their X-ray sources; 24 had two or three counterparts. match 16 of these to low-mass cluster members, all of For the latter group, we assume the X-ray emission to which are also detected in one or more of the previous originate from the closest match only. X-ray studies. We derive 0.5−7.0 keV LX values for these 8 Núñez & Agüeros sources using the available 0.2−4.5 keV (bands 1−4) in- youngest (6 Myr) and oldest (625 Myr) stars appear sig- strumental count rates. nificantly different from the rest. M stars behave simi- We search the XMM-Newton Upper Limit Server9 larly, although the evident differing completeness levels In total, there are 133 detected cluster stars, 94 of in this mass bin across clusters makes any interpretation which are low-mass cluster stars. For stars in more than of the M-star XLF and LLF difficult (e.g., the least mas- one X-ray study, we use a weighted average to calcu- sive star in the ONC is 0.10 M ; in NGC 6475, 0.52 M ). late the LX. The faintest detected cluster member has The varying sensitivity levels of the different cluster sur- a mass of 0.52 M . For all the stars in this cluster we veys hinder a straightforward comparison, as the derived −2 adopt d = 302 pc (van Leeuwen 2009), log(NH/cm ) = XLFs and LLFs of samples with lower sensitivities imply 20.54, and E(B − V ) = 0.06 (Robichon et al. 1999). populations that are more X-ray active than they should be (see e.g., Feigelson & Montmerle 1999; Preibisch & 4.1.6. The Hyades Zinnecker 2002; Feigelson et al. 2003). ROSAT PSPC (0.1−1.8 keV) observations of the 625- The unexpected behavior of the 120-Myr-old stars was Myr-old10 Hyades were first obtained by Stern et al. seen by Jeffries et al. (2006), who found that Pleiads have (1995), who examined a ≈30×30 deg area around the a similar level of activity as much older Hyads. That cluster center. These authors detected 188 Hyads and study, however, did not include any stars between the ages of the two clusters. Our inclusion of 220- and 490- measured LX ULs for 252 that remained undetected. Stelzer & Neuhäuser (2001) used publicly available Myr-old stars makes this odd result stand out. The XLF and LLF curves at 120 Myr are most left-shifted at lower PSPC data to report 0.1−2.0 keV LX for 191 Hyads, 36 of which were undetected by Stern et al. (1995). These values, suggesting that the explanation may lie in the differences in detection limits between the surveys. authors also measured LX ULs for 74 undetected cluster members, 40 of which were not in Stern et al. (1995). In Figure 5, the filled circles along each XLF and LLF We consolidate the two surveys and match the result- indicate the faintest X-ray source in each cluster at each ing list of X-ray sources to the Hyades catalog of Dou- mass bin. NGC 6475 and M37 have higher minimum glas et al. (2016), which combines the catalog of Gold- detection values than the 120-Myr-old sample. Further- man et al. (2013) with a handful of new Hyads identified more, the significant fraction of ULs in the 120-Myr-old from All Sky Automated Survey data (Cargile et al., in sample is also shifting the XLF toward lower LX, as we prep.). For our analysis, we considered only stars with found to be the case for M37 (see Figure 2). It is also possible that our XLF at 220 Myr implies a Pmem ≥70% in the Douglas et al. (2016) catalog. The result is 178 Hyads with detections and 82 with population that is over-luminous relative to reality, as our ULs, of which 143 and 79 are low-mass stars, respectively. sample of NGC 6475 stars does not include ULs. If this is The faintest detected Hyad has a mass of 0.13 M , and true, it would suggest that low-mass stars, and particu- larly K and M stars, do not decrease in X-ray luminosity the faintest Hyad with an LX UL, 0.18 M . For stars in both surveys, we use the weighted average count rate by a significant amount between 100 and 500 Myr. to calculate L . We use published star distances and In Figure 6, we plot the LX (top panels) and LX/Lbol X (bottom) K-M solutions for each cluster in the three mass assume negligible reddening and NH. For stars with no available distance, we set d = 46 pc (van Leeuwen 2009). bins with boxes and whiskers. Each box extends from the lower to the upper quartile, the horizontal line indi- 4.2. Results and Discussion cates the median value, and the whiskers span the entire data range for each cluster (Table 4 gives these K-M solu- Figure 5 shows the XLF (left panels) and LLF (right tions). The faintest X-ray source detected in each cluster panels) K-M solutions for M37 and the six clusters de- across the three mass bins is indicated with a red horizon- scribed above, with the Pleiades and NGC 2516 com- tal line in all panels. This corresponds to the minimum bined into a single 120-Myr-old cluster, for G (upper value for each cluster given in Column 4, Table 2. row), K (middle row), and M stars (bottom row). The The left panels shows the evolution of G stars, with the XLFs show an overall decrease in X-ray activity spanning X-ray minimum and maximum of the Sun (Peres et al. approximately two orders of magnitude from the age of 2000) indicated with black whiskers at 4.5 Gyr. A linear the ONC to that of the Hyades. G stars exhibit the most regression analysis in log space using the median values uniform decrease, as each subsequent cluster is approxi- (excluding the Sun) reveals a decrease in LX and LX/Lbol mately half an order of magnitude less luminous than the b c with time of the form LX ∝ t and LX/Lbol ∝ t previous one. The exception is the 120-Myr-old cluster, (black dashed lines), where b = −0.61 ± 0.12 and c = which is less luminous than this sequence would suggest, −0.68 ± 0.12. This is much shallower than the slope both in terms of its XLF and its LLF. quoted in Paper I (b = −1.23 ± 0.16), which included a K and M stars evolve less gradually. K stars between slightly different set of clusters and no ULs. The correla- 35−490 Myr decrease only very slightly in LX, while the tion coefficients of the fits are rb = −0.93 and rc = −0.94. Preibisch & Feigelson (2005) found a similar slope b = 9 http://xmm.esac.esa.int/UpperLimitsServer/ for data for the undetected low-mass clusters stars. However, we obtain only −0.76, but a shallower slope c ≈ −0.5, for their smaller one UL for one undetected NGC 6475 star. We derive the 0.5−7.0 sample of ONC, Pleiades, Hyades, and nearby field G keV LX UL value for this star from the EPIC-pn 0.2−2.0 keV count stars. On the other hand, Cargile et al. (2009) found rate UL estimated by this server. slopes b = −0.60 ± 0.01 and c = −0.64 ± 0.41 for their 10 Brandt & Huang (2015a,b) calculated the age of the cluster to be 750±100 Myr by fitting rotating stellar models to main-sequence sample of FG stars from 10 clusters spanning a similar turnoff Hyads. However, the quoted uncertainty does not include age range. Other studies of solar analogs that extend the additional ≈100 Myr systematic uncertainties mentioned by to ages >600 Myr have found a steeper slope b = −1.5 these authors. M37 and the Evolution of X-ray Emission in Low-Mass Stars 9

28 29 30 31 5 4 3 2 1 1.0 1.0 6 Myr (ONC) 35 Myr (NGC 2547) 120 Myr 0.8 220 Myr (NGC 6475) 0.8 490 Myr (M37) 625 Myr (Hyades) 0.6 0.6 G stars

0.4 0.4

0.2 0.2 Cumulative distribution function (K-M)

0.0 0.0

0.8 0.8

0.6 0.6 K stars

0.4 0.4

0.2 0.2 Cumulative distribution function (K-M)

0.0 0.0

0.8 0.8

0.6 0.6 M stars

0.4 0.4

0.2 0.2 Cumulative distribution function (K-M)

0.0 0.0 28 29 30 31 5 4 3 2 1 1 log(LX) (erg s− ) log(LX/Lbol) Fig. 5.— K-M estimator for the XLF (left panels) and LLF (right panels) of G, K, and M stars in the ONC (≈6 Myr), NGC 2547 (35 Myr), the merged NGC 2516 and Pleiades clusters (120 Myr), NGC 6475 (220 Myr), M37 (490 Myr), and Hyades (625 Myr). The LX values are all for 0.5−7 keV and derived from count rates applying a 1T-plasma model with 0.4 solar abundance and log(T /K) = 7. The filled circles indicate the minimum LX detected in each cluster at each mass bin. 10 Núñez & Agüeros

31 31 NGC2547 NGC2547 120 Myr Hyades M37 NGC6475 120 Myr 120 Myr NGC6475 Hyades NGC2547 30 M37 30 NGC6475 ) 1 M37 − Hyades s

g r ONC

e 29 29 (

) X L ( g o ONC l 28 28 Sun ONC 27 27 0.61 0.12 0.82 0.16 0.40 0.17 LX t− ± LX t− ± LX t− ± ∝ G stars ∝ K stars ∝ M stars

1 1 120 Myr ONC 2 NGC2547 2 ONC NGC6475 NGC6475 120 Myr M37 NGC6475 120 Myr NGC2547 M37 ) M37 l NGC2547

o 3 3 Hyades Hyades b L / X L

( 4 4 g o l ONC 5 5

6 Sun 6 Hyades 0.68 0.12 0.81 0.19 0.61 0.12 L /L t− ± L /L t− ± L /L t− ± 7 X bol ∝ X bol ∝ X bol ∝ 7 6.5 7.0 7.5 8.0 8.5 9.0 9.5 6.5 7.0 7.5 8.0 8.5 9.0 6.5 7.0 7.5 8.0 8.5 9.0 log(Age) (yr) log(Age) (yr) log(Age) (yr)

Fig. 6.— The evolution of LX (top panels) and LX/Lbol (bottom panels) for G, K, and M stars using the K-M estimator results. The representative 120 Myr-old cluster contains stars from NGC 2516 and the Pleiades. Each box extends from the lower to the upper quartile and the whiskers cover the entire data range. The median value is indicated by a horizontal line inside the box. The minimum X-ray value detected in each cluster across the three mass bins is indicated with a red horizontal line. In the G stars panels, the minimum and maximum of the Sun are indicated with black whiskers at 4.5 Gyr. The dashed lines indicate the linear regression analysis in log space (excluding the Sun) for each panel. The resulting dependencies of LX and LX/Lbol on age are given at the bottom of each panel. M37 and the Evolution of X-ray Emission in Low-Mass Stars 11

TABLE 4 Kaplan-Meier Statistics

−1 a Open log(LX)(erg s ) log(LX/Lbol) Cluster Min 25thb Median 75thb Max Min 25thb Median 75thb Max G stars ONC 29.58 30.00 30.18 30.70 31.03 -3.66 -3.54 -3.09 -2.56 -2.18 NGC 2547 29.33 29.65 29.89 30.16 30.49 -4.41 -3.87 -3.46 -3.22 -3.06 120 Myr 27.97 28.77 29.19 29.62 30.46 -5.46 -4.55 -4.28 -3.76 -2.70 NGC 6475 29.00 29.21 29.37 29.69 30.28 -4.62 -4.30 -4.00 -3.69 -2.69 M37 28.45 28.82 28.99 29.16 30.42 -5.09 -4.72 -4.58 -4.43 -3.00 Hyades 28.15 28.46 28.62 28.91 29.94 -5.30 -4.94 -4.73 -4.49 -3.19 K stars ONC 28.55 29.67 30.57 30.96 31.10 -4.40 -3.18 -2.21 -1.81 -1.69 NGC 2547 28.93 29.28 29.42 29.59 29.94 -3.70 -3.36 -3.24 -3.11 -2.80 120 Myr 28.44 28.66 29.08 29.35 30.14 -4.29 -4.09 -3.59 -3.30 -2.62 NGC 6475 28.64 29.15 29.37 29.68 30.00 -4.08 -3.43 -3.27 -3.04 -2.54 M37 28.73 28.82 28.91 29.15 29.92 -4.11 -4.09 -3.83 -3.57 -2.86 Hyades 27.63 27.63 28.18 28.66 29.46 -4.98 -4.92 -4.63 -4.06 -3.24 M stars ONC 27.82 29.03 29.48 29.95 31.41 -4.00 -2.39 -1.96 -1.65 -0.32 NGC 2547 28.83 29.10 29.26 29.40 30.46 -3.53 -3.19 -3.00 -2.83 -1.91 120 Myr 27.86 28.37 28.79 29.05 30.26 -4.25 -3.46 -3.19 -2.96 -1.25 NGC 6475 28.82 28.83 28.98 29.18 29.74 -3.63 -3.62 -3.39 -3.19 -2.55 M37 28.51 28.89 29.04 29.16 29.49 -3.67 -3.34 -3.13 -3.04 -2.64 Hyades 27.50 27.77 28.12 28.54 30.44 -4.84 -4.40 -3.65 -3.37 -0.86 a 0.5−7.0 keV band. b Lower and upper quartiles (i.e., 25th and 75th percentiles). (Maggio et al. 1987; Güdel et al. 1997; Giardino et al. evolution of these stars. 2008). Our linear regressions extrapolated to the age of Unlike in Figure 5, where the 120-Myr-old stars ap- the Sun over-predict the X-ray activity of solar-type stars pear under-luminous in X rays for their age compared at the solar age by ≈0.5 dex in both LX and LX/Lbol. to NGC 6475 and M37, Figure 6 and Table 4 show that The linear regression analysis for K stars in Figure 6 these stars do not deviate much from the general trend (center panels) indicates that LX and LX/Lbol decrease observed from 6 to 625 Myr. It is therefore very likely following the LX(t) and LX/Lbol(t) relations described that the somewhat unexpected shape of the XLF at 120 above with slopes b = −0.82 ± 0.16 (rb = −0.93) and c = Myr is mostly a construct of the lower sensitivity and −0.81±0.19 (rc = −0.91). These are statistically similar completeness of the NGC 6475 and M37 X-ray surveys to the slopes found for G stars. Although our value for relative to those of the Pleiades and NGC 2516. b agrees with that of Preibisch & Feigelson (2005, b = Is a linear fit adequate for the full age range we con- −0.78) and of Cargile et al. (2009, b = −0.62 ± 0.27) for sider? Clearly, we do not have enough points in age space their samples of K stars, our c slope is steeper than these to explore fitting broken power laws with different slopes authors’ (c ≈ −0.5 and c = −0.34 ± 0.32, respectively). for different age ranges. Instead, we redo the linear re- The relations found for M stars (right panels) have gression analysis by excluding open clusters that either slopes b = −0.40±0.17 (rb = −0.76) and c = −0.61±0.12 should or appear to behave differently from the others. (rc = −0.93), the former being statistically different from For instance, even though we exclude ONC stars with cir- that of K stars. Otherwise, these slopes are all within one cumstellar disks or strong accretion (see Section 4.1.1), standard deviation of the results for the other mass bins. X-ray emission from this cluster may still not be truly Preibisch & Feigelson (2005) found a steeper slope b = comparable to that of older clusters, as its low-mass PMC −0.69, while Cargile et al. (2009) had a shallower slope members may be spinning up on their way to the main of b = −0.30±0.21, for their M stars. Analogously to the sequence. At the other end of our age range, Hyades case of G stars beyond the age-range we studied, Stelzer stars may have already passed an evolutionary threshold et al. (2013) found a steeper slope b = −1.10 ± 0.02 beyond which X-ray activity decreases at a faster pace, for a sample of M0−M3 stars in the solar neighborhood as seen in studies of older clusters such as the >1-Gyr-old covering the ages 0.1−3 Gyr. cluster NGC 752 (Giardino et al. 2008). In LX/Lbol space, however, our slope c is significantly Linear fits in log space for LX and LX/Lbol excluding steeper than the slopes found by Preibisch & Feigel- the ONC result in slightly steeper slopes for all mass bins son (2005) (c ≈ −0.3) and Cargile et al. (2009) (c = except for K stars in LX space and M stars in LX/Lbol −0.08 ± 0.26). In the framework of the rotation-activity space; the latter results in a slope shallower by a fac- relation, the similar decay in X-ray activity we find for M tor of two. However, the new slopes lie well within one and GK stars may suggest that even if a different brak- standard deviation of the original fits, and they all have ing mechanism operates for fully convective stars (spec- worse (i.e., closer to zero) rb and rc values than the orig- tral types ≈M6 and later), the decay in coronal heating inal fits. This suggests that the overall X-ray activity of nonetheless occurs at the same rate as in stars with ra- such young stars does not significantly deviate from the diative cores. The evident incompleteness at the lowest general decaying trend observed in the first 600 Myr of masses in several of the clusters studied here prevents us, their lives. however, from making any strong claims about the X-ray On the other hand, linear fits excluding the Hyades 12 Núñez & Agüeros result in slightly shallower slopes for all three mass bins. two orders of magnitude, as indicated by their median LX Again, the new slopes lie within one standard deviation and LX/Lbol values, whereas M stars decrease by about of the original fits, and they all have very similar rb and rc 1.5 orders of magnitude. values. Therefore, we see no evidence that the behavior The XLFs and LLFs of stars at 120 Myr (NGC 2516 of stellar coronae has changed significantly by the time and the Pleiades combined) appear under-luminous com- low-mass stars reach the age of the Hyades. However, the pared to that of younger and older clusters. This is likely scarcity of well-characterized >1-Gyr-old open clusters to be the result of the large number of ULs included in prevents us from conducting a more detailed study of these XLFs and LLFs and of the relatively higher detec- a hypothetical distinct late evolutionary stage of stellar tion sensitivity of the X-ray surveys of the Pleiades. activity beyond 625 Myr. Conversely, the XLFs and LLFs of NGC 6475 may be Finally, we examine whether assuming the same 107 K the anomalous ones, as the lack of ULs in this cluster coronal temperature for all stars in the age range 6−625 may make it seem over-luminous for its age. These re- Myr significantly impact our results. For the youngest sults highlight the difficulty in comparing X-ray surveys stars in our sample (i.e., ONC members), doubling the with different sensitivities and completeness. Most clus- representative plasma temperature decreases the derived ters included here deserve deeper X-ray studies to fully LX values by 0.03−0.77 dex; the larger the value of NH, characterize the evolution of activity in low-mass stars. the larger the decrease. For the oldest stars in our sample The decay rate over the approximate age range 6−625 (i.e., Hyads), cutting the temperature in half decreases Myr is well described by a single linear fit in log space. b the derived LX values by 0.17 dex (see Appendix for fur- The decay follows the relation LX ∝ t , with b = ther discussion). The effect of these decreased LX values −0.61 ± 0.12 for G stars, −0.82 ± 0.16 for K stars, and at ≈6 Myr and 625 Myr on the age-activity relations of −0.40 ± 17 for M stars. In LX/Lbol space, the decay fol- c Figure 6 is inconsequential: the largest change in fitted lows LX/Lbol ∝ t , with c = −0.68 ± 0.12 for G stars, parameters is the slope c for M stars, which becomes −0.81 ± 0.19 for K stars, and −0.61 ± 0.12 for M stars. slightly steeper (−0.69 ± 0.18). We are therefore confi- The incompleteness of the M star data in several clus- dent that our decision to chose one representative plasma ters prevents us from making any strong conclusions, but temperature is reasonable for this analysis. our results are incompatible with the paradigm of slower rotational decay rates for M stars compared to G or K 5. CONCLUSION stars. Based on our data, the difference in braking mech- We use a 440.5 ks Chandra observation of M37 to char- anisms between fully convective mid- to late-type M stars acterize the XLFs and LLFs of <1.2 M stars at 490 Myr. and GK stars with radiative cores manifests itself only In Paper I we detected 162 such stars; here we add ULs marginally in the coronal heating process. for 160 cluster stars that were undetected in our original The decay rates in LX and LX/Lbol for G stars over- observations. At 490 Myr, these G, K, and M stars ex- predict the X-ray activity of the Sun. This, together with hibit similar levels of X-ray activity (median log(LX) ≈ existing results from solar analogs with t > 1 Gyr show- 29.0 erg s−1) with similar statistical spreads (28.8−29.2 ing b = −1.5, suggests that at older ages than those sam- as the lower−upper quartiles). In LX/Lbol space, on the pled here the age-activity relation may be significantly other hand, we find that more massive stars produce steeper for solar-mass stars. Excluding the Hyades from a smaller fraction of their overall energy output in the our linear fits results in slightly shallower slopes but sim- X ray, with median LX/Lbol values of −4.73, −3.83, and ilar statistical fits for all three mass bins. Thus, if there −3.13 for G, K, and M stars, respectively. is a more rapid decline in X-ray activity at older ages, it To characterize the evolution of X-ray activity, we com- appears to take place beyond 625 Myr. pare the M37 XLFs and LLFs to those of other open clus- ters in the approximate age range 6−625 Myr: the ONC, NGC 2547, NGC 2516, the Pleiades, NGC 6475, and the Hyades. We homogenize the X-ray data from different We thank Vinay Kashyap for his insights into UL com- surveys by converting published count rates into energy putations and K-M estimations, and Jeremy Drake for fluxes using the same model and parameter values: a 1T his comments on constructing XLFs. We thank the APEC model with 0.4 solar abundance and log(T /K) = anonymous referee for comments that helped improve 7. As in other studies, we find that this choice of tem- the paper. We thank the SAO Pre-doctoral Program perature is an adequate approximation for active stars for hosting A.N. for three months at the Harvard Smith- detected as low-count X-ray sources. sonian Center for Astrophysics in Cambridge, MA. This We use up-to-date cluster reddening and distance mea- research has made use of data obtained from the 3XMM surements to calculate NH and LX, respectively. We ob- XMM-Newton serendipitous source catalogue compiled tain the masses for members of all clusters by apply- by the 10 institutes of the XMM-Newton Survey Science ing the same photometric color-mass relation, except for Centre selected by ESA. Support for this work was pro- stars in the ONC, for which we use previously published vided by NASA through Chandra Award Number G02- masses. Finally, we calculate Lbol from a linear interpo- 13025A issued by the Chandra X-ray Observatory Cen- lation between mass-Lbol values we derive for M37 stars. ter, which is operated by the Smithsonian Astrophysical The XLFs and LLFs of stars in the approximate age Observatory for and on behalf of NASA under contract range 6−625 Myr shift toward lower luminosities over NAS8-03060. M.A.A. acknowledges support provided by time. G and K stars decrease in X-ray activity by almost the NSF through grant AST-1255419.

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APPENDIX IS IT APPROPRIATE TO USE T = 107 K TO MODEL CORONAE FOR LOW-MASS STARS RANGING FROM 6 TO 600 MYR IN AGE? In Section 2.3, we model the X-ray emission for all the stars in our sample using a single coronal temperature of T = 107 K. This implies minimal evolution of this temperature for low-mass stars from 6 to 625 Myr, which is somewhat surprising: higher T values may be more appropriate for the youngest stars and lower T values for the oldest. Here, we investigate the effect of varying the coronal temperature: we cut our benchmark T in half for the 14 Núñez & Agüeros

TABLE A1 Impact of Using Different Coronal T Values on Linear Regression Fits to the Age-Activity Relation

Coronal G Stars K Stars M Stars Temperature Slope Slope Slope

LX v. t T = 107 K −0.61 ± 0.12 −0.82 ± 0.16 −0.40 ± 0.17 Alternative T a −0.61 ± 0.15 −0.83 ± 0.23 −0.46 ± 0.26

LX/Lbol v. t T = 107 K −0.68 ± 0.12 −0.81 ± 0.19 −0.61 ± 0.12 Alternative T a −0.61 ± 0.15 −0.80 ± 0.23 −0.69 ± 0.18 a T = 5 × 106 K for Hyads, T = 2 × 107 K for ONC stars, and T = 107 K for all other stars in our sample. oldest stars in our sample (i.e., Hyads), double it for the youngest ones (i.e., ONC stars), and keep T = 107 K for all other stars. We find that cutting T in half for the Hyads leads to the derived LX values decreasing by 0.17 dex. The LX values −2 also decrease when we double T for the ONC stars, albeit as a function of NH, which ranges from 20 < log(NH/cm ) −2 < 23 for this cluster (for the Hyades, NH is negligible). For log(NH/cm ) values of 20, 21, 22, and 23, LX decreases −2 by 0.03, 0.06, 0.30, and 0.77 dex, respectively. In our ONC sample, 42% of stars have log(NH/cm ) < 21, 91% have −2 −2 log(NH/cm ) < 22, and 100% have log(NH/cm ) < 23, so that for the bulk of these stars the decrease is <0.30 dex. We then test how much the age-activity linear regression fits described in Section 4.2 change if we use the halved and doubled T values for Hyads and ONC stars. Table A1 compares the original fits based on an assumed T = 107 K for all stars in our sample to fits using the new LX values derived for Hyads and ONC stars. We find that assuming different coronal temperatures for our two bookend clusters does not have a significant impact on our results. To first approximation, T = 107 K is an appropriate choice for the plasma temperature for the stars in our sample over the age range 6−625 Myr.